Why wouldn't hole through earth work?

[Nevermore]

I know that a hole through the earth wouldn't work because it constitutes perpetual motion. But what exactly would stop you from falling, reaching terminal velocity, falling the other direction, reaching terminal velocity again and oscilating like that forever? It couldn't be friction, air doesn't stop you from reaching terminal velocity if you jump out of a plane. Does terminal velocity not bring you far enough into the other side of the earth to reach it again?

 

Long post, I know.

[insane_alien]

ok, there are a few things that would stop you.

1/ air resistance. you mention this but you don't take into account that the friction would increase as you descend due to increase in density of the air and a decreasing force of gravity. because of this, you would just slow odwn gradually eventually stopping at the centre.

 

2/ the earths rotation. if falling for long enough you're eventually going to collide with the side and it would likely be painful and fatal.

 

It couldn't be friction, air doesn't stop you from reaching terminal velocity if you jump out of a plane.

its friction that causes terminal velocity. terminal velocity is where the force of gravity and the drag force equalise. you can change your terminal velocity by the way you fall. starfish shaped and you go slow. head first like a missile and you go fast.

[ecoli]

Well, you can't exactly drill a whole in the earth. I think that would be the main limitation.

[Sisyphus]

Well, at the center of the Earth, the force of gravity is zero, and therefore terminal velocity is zero. However, even assuming gravity was constant all the way through, and you pass the center at the same terminal velocity you have on the surface, you wouldn't get high enough on the other side to reach the same speed coming back. You would have to have all of your kinetic energy convert to potential, which of course you wouldn't since there would be friction.

 

However, if there was no air in the tube and therefore no friction (impossible to do perfectly, but so is drilling a hole through the Earth), you would yoyo back and forth forever, just reaching both surfaces. It's not really a "perpetual motion machine" because you're not getting any more energy out of the system than you start with.

[timo]

Well, at the center of the Earth, the force of gravity is zero, and therefore terminal velocity is zero.

I dunno what you call "terminal velocity" but saying that if acceleration (gravity) is zero, then velocity is zero at least needs some further comment as it´s not obvious without knowing how the statement is meant or in what context it appears. Assuming terminal velocity is supposed to be the velocity which you´d reach the center of earth, then your statement is wrong, for example.

 

... and you pass the center at the same terminal velocity you have on the surface, ...

I still don´t know what you call "terminal velocity" but I think we can safely assume that the velocity at the surface shall be zero, which certainly is not the velocity with which you´ll pass by the center of earth.

 

However, if there was no air in the tube and therefore no friction (impossible to do perfectly, but so is drilling a hole through the Earth), you would yoyo back and forth forever, just reaching both surfaces. It's not really a "perpetual motion machine" because you're not getting any more energy out of the system than you start with.

Correct (felt like I should say something non-destructive ). Note: Yoyoing back and forth forever without having to put in any (or very little) energy would be a great improvement for long-distance travels (in comparison for cars and planes, for example).

[Severian]

I always find this to be one of the slighly wierd misconceptions the general public have about physics - that somehow physics prevents perpetual motion.

 

It is really the other way around. Physics tells us that the natural state of an object is perpetual motion. If an object is moving, and no forces are acting on it, it will continue to move forever. If you want to stop this perpetual motion, you have to apply a force to stop it (e.g. friction).

[swansont]

I always find this to be one of the slighly wierd misconceptions the general public have about physics - that somehow physics prevents perpetual motion.

 

It is really the other way around. Physics tells us that the natural state of an object is perpetual motion. If an object is moving' date=' and no forces are acting on it, it will continue to move forever. If you want to stop this perpetual motion, you have to apply a force to stop it (e.g. friction).[/quote']

 

The general public are more familar with a badly-worded version of the second law of thermodynamics than they are with the second law of Newtonian motion.

[timo]

I always find this to be one of the slighly wierd misconceptions the general public have about physics - that somehow physics prevents perpetual motion.

Doesn´t it, in the end? By "perpetual motion" I´d think of a system that reaches it initial state after some time (so I wouldn´t count an asteroid flying in a straight line through void). In the case given here, we´d have air resistance. The energy lost through it cannot brought back to the system. An example without air resistance could be a planet orbiting a sun. Now, I´ve never seen or even done the actual calculation but I think there was the prediction that massive objects orbiting each other emit gravitational waves so you´d lose energy over time. Same goes for an electron orbiting a nucleus when viewing it classically (EM waves here, of course) - using QM won´t help unless you have a good argument why you call a groundstate "motion". I assume you´d even have some loss of energy due to gravitational waves in the case of the yoyoing train through earth.

 

I know that wasn´t your point, but I am not really sure that when you take all physics effects into account, perpetual motion (in the sense of above) can really exist - not even in idealized models such as "no air resistance". But I cannot proof that they cannot, either (might be possible by using thermodynamics, though).

 

One perpetual motion system in above sense I could actually think of (even if it´s very far-fetched): An asteroid moving through an otherwise completely empty universe with a toroidal topology

[YT2095]

actualy I don`t think that at the center of the Earth there is No gravity, it seems ilogical.

rather there IS gravity but it would be pulling on you equaly in all directions, as if trying to pull you appart. the net effect would SEEM like there is no gravity though.

[woelen]

No, there really IS no force, there is nothing trying to pull you apart. The forces nicely neutralize each other.

 

Compare this with an electrical circuit. If I take two equal resistors R in series and I apply a voltage V to one resistor and a voltage -V to the other resitor, then at the node, between both resistors the voltage is equal to 0. The voltages precisely cancel. One cannot tell the difference between this situation and a situation, where a resistor R/2 is connected to the GND wire. Exactly the same is true in the center of the earth. A blinded observer, who only can feel gravity could not observe any difference between the centre of the earth and deep space (disregarding the enormous temperature and pressure of course ).

[timo]

actualy I don`t think that at the center of the Earth there is No gravity' date=' it seems ilogical.

rather there IS gravity but it would be pulling on you equaly in all directions, as if trying to pull you appart. the net effect would SEEM like there is no gravity though.[/quote']

Given that there is no difference (you only "see" the sum of all forces), you can pretty much view it however you want. It´s often more elegant to take the stance that the charge distributions ("charge" being used as a generic term here, in this case the charge is mass) create a potential field [math]V(\vec x)[/math]. This is especially nice if you are considering energy conservation - in the case of the OP you could easily get the velocity at the center of earth by looking at the difference in potential between the center and the surface, for example. The force then is simply the derivative of the potential with respect to position times the charge (here: [math] \vec F = -(\partial_x \ \partial_y \ \partial_z) m V(\vec x) [/math] ). Here, the constituents (gravity pulling equally from all sides) are hidden and in some sense lost in the potential function V.

But asked along the other way round: How would you differ between "there is gravity" and "there is no gravity" other than looking if the net force is zero? In a way that you can experimentally tell a difference, I mean.

[YT2095]

but the point at which this is true is so incredibly Tiny, that anywhere to either side of this point it wouldn`t be true.

 

for instance, if the cavity was large in the middle, say 1/3 the earths diameter, it would be possible to walk all around the inside sphere.

[swansont]

but the point at which this is true is so incredibly Tiny' date=' that anywhere to either side of this point it wouldn`t be true.

 

for instance, if the cavity was large in the middle, say 1/3 the earths diameter, it would be possible to walk all around the inside sphere.[/quote']

 

 

No, you wouldn't be able to walk, since there would be no force to hold you to the surface. There would be no gravity in the entire void region, assuming the mass on the outside were evenly distributed.

[5614]

Ye, to move on the surface of the Earth you push backwards against the ground and the ground pushes you forward. If you're "floating" in the center of the Earth then there's nothing to push against, so you can't move.

 

I prefer to think of it as the sum of all forces equalling zero. There is mass around you, to say there is no gravity just sounds wrong, to me, it's like saying "yes there's mass but there is no gravity", it goes against the "all mass has a gravitational field" thing.

[Sisyphus]

I dunno what you call "terminal velocity" but saying that if acceleration (gravity) is zero, then velocity is zero at least needs some further comment as it´s not obvious without knowing how the statement is meant or in what context it appears. Assuming terminal velocity is supposed to be the velocity which you´d reach the center of earth, then your statement is wrong, for example.

 

I take "terminal velocity" to mean the equilibrium velocity at which the force of gravity is equal to the force of air resistance, resulting in zero acceleration. If there is no force of gravity but there is air, any moving object will eventually slow to a stop (there only being zero air resistance when motionless), making zero its "terminal velocity."

 

I still don´t know what you call "terminal velocity" but I think we can safely assume that the velocity at the surface shall be zero, which certainly is not the velocity with which you´ll pass by the center of earth.

 

Again, terminal velocity is when mg = air resistance. In order to have the same terminal velocity at the surface as everywhere else, g would have to not change. Obviously it would, but I was allowing it for the sake of argument.

[insane_alien]

Sisyphus, you forgot to add in the changes on the other side of the equation. terminal velocity for any arbitrary object at 10000 ft is greater than terminal velocity at 5000ft due to density changes in the air.

[Sisyphus]

but the point at which this is true is so incredibly Tiny' date=' that anywhere to either side of this point it wouldn`t be true.

 

for instance, if the cavity was large in the middle, say 1/3 the earths diameter, it would be possible to walk all around the inside sphere.[/quote']

 

There is no gravity anywhere inside a hollow sphere of uniform thickness, no matter what the size of the sphere or of the hollow.

 

To demonstrate:

Imagine you are somewhere within this hollow. Draw a line through both yourself and the center, then make that line the axis of a conic section such that a circle of matter is within the section on both the near and far sides of the sphere. Since the section is the same angle on both sides, it is the gravity of the one section that is pulling against the other. These forces are always equal, because gravity decreases with the square of distance, but the area in each section increases with the square of your distance from it.

[Sisyphus]

Sisyphus, you forgot to add in the changes on the other side of the equation. terminal velocity for any arbitrary object at 10000 ft is greater than terminal velocity at 5000ft due to density changes in the air.

 

Yeah, I ignored that because it only makes what I was saying more true. As g decreases, air resistance increases, meaning terminal velocity will drop off even faster. But it's still zero in the center.

[swansont]

Ye' date=' to move on the surface of the Earth you push backwards against the ground and the ground pushes you forward. If you're "floating" in the center of the Earth then there's nothing to push against, so you can't move.

 

I prefer to think of it as the sum of all forces equalling zero. There is mass around you, to say there is no gravity just sounds wrong, to me, it's like saying [i']"yes there's mass but there is no gravity"[/i], it goes against the "all mass has a gravitational field" thing.

 

But it's exactly the same as there being no electric field inside of a uniformly charged spherical surface that contains no charge inside.

[5614]

But it's exactly the same as there being no electric field inside of a uniformly charged spherical surface that contains no charge inside.

But that's because the charge has moved to the outside. Whereas inside a plannet the gravitational fields have cancelled.

 

Am I wrong? Or is there no difference between the two?

[Sisyphus]

Well the gravity of everything in the entire universe is acting on you at all times, but we still say that it has a direction (down) and a magnitude, just because that's the net gravity and everthing else pretty much cancels out.

[swansont]

But that's because the charge has moved to the outside. Whereas inside a plannet the gravitational fields have cancelled.

 

Am I wrong? Or is there no difference between the two?

 

No difference; both are applications of Gauss's law. In the charge case it need not be a conductor — it would work if you just scooped out the center of a uniformly charged material, analogous to tunneling out the center of the earth.

[5614]

No difference; both are applications of Gauss's law. In the charge case it need not be a conductor — it would work if you just scooped out the center of a uniformly charged material, analogous to tunneling out the center of the earth.

Good, so you can equally argue both "there is no charge" and "it has all cancelled itself out" and at the end of the day there is no difference.

 

So the way I've though of as gravity cancelling itself out whilst there is no electric charge inside a uniformly charged sphere is fine.

[CanadaAotS]

Ok...

 

you're falling down the hole.

 

A few assumptions to make things simple:

 

a) no air. Lets pretend its a vacuum

b) intense heat etc. doesnt kill you near the center

c) the earths mass around the hole is perfectly distrubuted as a sphere

 

The force of earths mass pulling you to the center becomes less and less the closer to the center you get. If you also pretend that you are a perfect sphere your self (or at least perfectly symetrical) then what will happen is when you pass directly at the center of earth your change in velocity will be 0, but your actual velocity will be some arbitary (and probably very high) number. From the center on the earth is pulling you back towards the center and the farther from the center you get, the more earth there is pulling you down. so G (being force of gravity) is increasing. As your velocity slows down more and more it will reach 0 RIGHT when you reach the surface on the otherside, and then you yo-yo all the way back down.

 

Eventually you'll end up colliding with a side though, since the rest of the mass in the universe is effecting you lol.

 

Now, you can add all the assumptions back if you like. If you add air resistance, the air resistance will become greater and greater the closer to the center you get, hence your terminal velocity will increase. Your terminal velocity will NOT hit 0 however. The only time terminal velocity goes to 0 is when you hit a brick wall haha

 

A few people dont seem to understand what terminal velocity is... Its when Force of friction and the Force of Gravity equalize and cancel each other out (exactly why you stay at the same velocity, no acceleration is happening).

 

Because Ff is increasing and Fg is decreasing the point they equalizing gets smaller real fast.

 

Thats pretty much my 2 cents in the matter.

Just a question, I forget how to use the fancy equation text, what are the tags for it again? lol

[5614]

CanadaAotS: you wanna use the [math] tags!